The present application relates generally to an improved data processing apparatus and method and more specifically to an apparatus and method for a gradient-based search mechanism for optimizing photolithograph masks.
Optical lithography is a crucial step in semiconductor manufacturing. The basic principle of optical lithography is quite similar to that of chemistry-based photography. The images of the patterned photo-mask are projected through the high-precision optical system onto the wafer surface, which is coated with a layer of light-sensitive chemical compound, e.g. photo-resist. The patterns are then formed on the wafer surface after complex chemical reactions and follow-on manufacturing steps, such as wet or dry etching.
The resolution of the photo-lithography system (R) can be described by the well-known Rayleigh's equation:
  R  =                    k        1            ⁢      λ        NA  in which λ is the wavelength of the light source, NA is the numerical aperture and k1 is the factor describing the complexity of resolution enhancement techniques. As the very-large-scale integration (VLSI) technology pushes further into nanometer region, the feasible wavelength of the photo-lithographic system remains unchanged at 193 nm. Although there is anticipation that extreme ultraviolet lithography (EUVL) with the wavelength of 13 nm will replace traditional optical lithography, the availability of EUVL remains uncertain due to technical challenges and cost issues. On the other hand, the physical limit of dry lithography of NA is 1.0. The recently introduced immersion lithography has bigger NA (1.2), but it is harder to achieve higher NA values. Thus it is commonly recognized that k1 remains a cost effective knob to achieve finer resolution.
Due to the unavoidable diffraction, the optical lithography system is lossy in the sense that only low frequency components of the electromagnetic field can pass the optical system. As the gap between the required feature size and lithography wavelength gets bigger, the final wafer images are quite different from the patterns on the mask. In the past few years, resolution enhancement techniques (RETs) have become necessary in order to achieve the required pattern density. One well-known RET is the optical proximity correction (OPC), in which the mask patterns are intentionally “distorted” so that the desired image can be formed on the wafer. Other commonly used RETs are sub-wavelength resolution assist features (SRAF) and phase-shift masks (PSM). Nowadays, considerable amount of computing power has to be dedicated to these post-layout processes (often referred as data prep). Large computer farms have to spend weeks of central processing unit (CPU) time to perform data prep after a design is completed. However, all these RET methods have one significant drawback: there is no guarantee the achieved results will be optimal. Furthermore, as the technology is further pushed, manufacturing variations (e.g., dose and focus variations during the lithograph steps) have to be considered. However, it is quite challenging to systematically incorporate the process variations into the traditional RETs.
On the other hand, this particular problem can be considered from a different angle. Instead of locally perturbing the pattern to compensate for the loss, the mask pattern may be treated as the input to the optical system, and the wafer image as the output. The task then becomes how to “design” a mask so that the desired wafer image can be formed. This concept is often referred as “image design”, and was proposed over 20 years ago. However, the problem itself is often ill-posed in the sense that more than one input can generate the same output. It can be shown that the size of the search space is well over 21,000,000 which is even larger than the number of atoms in the observable universe. There were some early attempts to find a feasible solution to this problem by using method such as simulated annealing, genetic algorithms, and random pixel flipping. In recent years, the growing challenges facing sub-wavelength lithography and the ever increasing complexity of traditional RETs have made this idea more attractive, which is often referred as “inverse lithography” or “computational lithography”. A gradient search based method was proposed to overcome the excessive computational cost. However, the proposed method used non-realistic assumptions regarding the optical system (incoherent and coherent), while it is well-recognized that partially coherent models are the only acceptable model for the optical lithography system. Furthermore, the method was not demonstrated in a true industrial lithography environment.